I'm currently teaching how to calculate volumes of revolution using integration,
for e.g. suppose f(x)=x^2 is rotated 360 degrees about the x-axis from x = 2 to x=4, the volume generated would be given by
What I'm trying to do is plot the generated volume for explanation and demonstration purposes.
some of the more complicated examples are something like,
The region bounded by the curve y=9-x^2, x=2 and the x-axis is rotated 2Pi radians about the y-axis, calculate the volume of the solid generated.
I know how to calculate the actual volume, but is there any easy way of plotting the solid formed in mathematica.